Combinatorics practice problems

Q1 - How many 4-letter words can be made from the letters of 'EXAMINATION'?
Solution:
Total: 11 letters
1E, 1X, 2A, 1M, 2I, 2N, 1T, 1O

Case 1: All different: 8C4*4! = 1680
Case 2: 2 Same, 2 different: 3C1.7C2.4!/2! = 756
Case 3: 2 Same, 2 Same: 3C2.4!/2!

Q2 - How many 5 letter words using letters of 'INTEGRATION'?
Solution:
Total 11 letters.
2I, 2N, 2T, 1E, 1G, 1R, 1A, 1O
Case 1: All 5 different = 8C5*5!
Case 2: 2 Same, 3 Diff = 3C1*7C3*5!/2!
Case 3: 2 Same, 2Same, 1 diff = 3C2.6C1.5!/2!2!

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